TY - JOUR

T1 - MATHEMATICS AS A QUASI-EMPIRICAL SCIENCE

AU - Oliveri, Gianluigi

PY - 2006

Y1 - 2006

N2 - The present paper aims at showing that there are times when set theoretical knowledge increases in a non-cumulative way. In other words, what we call 'set theory' is not 'one' theory which grows by simple addition of a theorem after the other, but a finite sequence of theories T(1),..., T(n) in which T(i+1) supersedes T(i). This thesis has great philosophical significance because it implies that there is a sense in which mathematical theories, like the theories belonging to the empirical sciences, are fallible and that, consequently, mathematical knowledge has a quasi-empirical nature. The way I have chosen to provide evidence in favour of the correctness of the main thesis of this article consists in arguing that Cantor-Zermelo set theory is a Lakatosian Mathematical Research Programme (MRP).

AB - The present paper aims at showing that there are times when set theoretical knowledge increases in a non-cumulative way. In other words, what we call 'set theory' is not 'one' theory which grows by simple addition of a theorem after the other, but a finite sequence of theories T(1),..., T(n) in which T(i+1) supersedes T(i). This thesis has great philosophical significance because it implies that there is a sense in which mathematical theories, like the theories belonging to the empirical sciences, are fallible and that, consequently, mathematical knowledge has a quasi-empirical nature. The way I have chosen to provide evidence in favour of the correctness of the main thesis of this article consists in arguing that Cantor-Zermelo set theory is a Lakatosian Mathematical Research Programme (MRP).

KW - Cantor-Zermelo set theory

KW - Lakatos

KW - mathematical knowledge

KW - mathematical research programmes

KW - philosophy of mathematics

KW - quasi-empiricism and mathematics

KW - Cantor-Zermelo set theory

KW - Lakatos

KW - mathematical knowledge

KW - mathematical research programmes

KW - philosophy of mathematics

KW - quasi-empiricism and mathematics

UR - http://hdl.handle.net/10447/10378

M3 - Article

VL - 11

SP - 41

EP - 79

JO - Foundations of Science

JF - Foundations of Science

SN - 1233-1821

ER -